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%TCIDATA{Created=Mon May 10 13:44:37 2004}
%TCIDATA{LastRevised=Wednesday, June 11, 2008 09:32:29}
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\newtheorem{theorem}{Theorem}
\newtheorem{acknowledgement}[theorem]{Acknowledgement}
\newtheorem{algorithm}[theorem]{Algorithm}
\newtheorem{axiom}[theorem]{Axiom}
\newtheorem{case}[theorem]{Case}
\newtheorem{claim}[theorem]{Claim}
\newtheorem{conclusion}[theorem]{Conclusion}
\newtheorem{condition}[theorem]{Condition}
\newtheorem{conjecture}[theorem]{Conjecture}
\newtheorem{corollary}[theorem]{Corollary}
\newtheorem{criterion}[theorem]{Criterion}
\newtheorem{definition}[theorem]{Definition}
\newtheorem{example}[theorem]{Example}
\newtheorem{exercise}[theorem]{Exercise}
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{notation}[theorem]{Notation}
\newtheorem{problem}[theorem]{Problem}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{remark}[theorem]{Remark}
\newtheorem{solution}[theorem]{Solution}
\newtheorem{summary}[theorem]{Summary}
\newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}}
\begin{document}
Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{4}x^{4}-64}{x^{2}-9}}{\dfrac{a^{4}x^{2}+8}{x^{2}-x-6}}%
\]
se obtiene:\newline$\qquad$a) $\allowbreak\left(  x+2\right)  \dfrac
{a^{4}x^{4}-64}{\left(  a^{4}x^{2}+8\right)  \left(  x+3\right)  }\qquad$b)
$\left(  x-2\right)  \dfrac{a^{14}x^{4}-64}{\left(  a^{4}x^{2}+8\right)
\left(  x+3\right)  }$\newline\qquad c) $\left(  x+2\right)  \dfrac
{a^{16}x^{4}-64}{\left(  a^{4}x^{2}+8\right)  \left(  x-3\right)  }\qquad$d)
$\left(  x-2\right)  \dfrac{a^{16}x^{4}-64}{\left(  a^{4}x^{2}-8\right)
\left(  x+3\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{x^{2}-64}{x^{2}-16}}{\dfrac{x^{2}-8x+16}{x^{2}-x-5}}%
\]
se obtiene:\newline$\qquad$a) $\allowbreak\left(  x+8\right)  \left(
x-8\right)  \dfrac{x^{2}-x-5}{\left(  x-4\right)  ^{3}\left(  x+4\right)
}\qquad$b) $\left(  x+8\right)  \left(  x-8\right)  \dfrac{x^{2}-x-5}{\left(
x+4\right)  ^{3}\left(  x-4\right)  }$\newline\qquad c) $\left(  x+8\right)
\left(  x-8\right)  \dfrac{x^{2}+x-5}{\left(  x-4\right)  ^{3}\left(
x+4\right)  }\qquad$d) $\left(  x+8\right)  \left(  x-8\right)  \dfrac
{x^{2}-x+5}{\left(  x-4\right)  ^{3}\left(  x+4\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{x^{2}-9x+20}{x^{2}-16}}{\dfrac{x^{2}-8x+16}{x^{2}-4x-5}}%
\]
se obtiene:\newline$\qquad$a) $\allowbreak\left(  x+1\right)  \dfrac{\left(
x-5\right)  ^{2}}{\left(  x-4\right)  ^{2}\left(  x+4\right)  }\qquad$b)
$\left(  x-1\right)  \dfrac{\left(  x-5\right)  ^{2}}{\left(  x-4\right)
^{2}\left(  x+4\right)  }$\newline\qquad c) $\left(  x-1\right)
\dfrac{\left(  x+5\right)  ^{2}}{\left(  x-4\right)  ^{2}\left(  x+4\right)
}\qquad$d) $\left(  x+1\right)  \dfrac{\left(  x+5\right)  ^{2}}{\left(
x-4\right)  ^{2}\left(  x+4\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{x^{2}-9x+20}{x^{2}-1}}{\dfrac{x^{2}-8x+16}{x^{2}-4x-5}}%
\]
se obtiene:\newline$\qquad$a) $\allowbreak\dfrac{\left(  x-5\right)  ^{2}%
}{\left(  x-4\right)  \left(  x-1\right)  }\qquad$b) $\left(  x-1\right)
\dfrac{\left(  x-5\right)  ^{2}}{\left(  x-4\right)  \left(  x+1\right)  }%
$\newline\qquad c) $\dfrac{\left(  x-5\right)  ^{2}}{\left(  x-4\right)
\left(  x+1\right)  }\qquad$d) $\dfrac{\left(  x+5\right)  ^{2}}{\left(
x-4\right)  ^{2}\left(  x+1\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{x^{2}-7x+10}{x^{2}-4}}{\dfrac{x^{2}-8x+16}{x^{2}-4x-5}}%
\]
se obtiene:\newline$\qquad$a) $\left(  x+1\right)  \allowbreak\dfrac{\left(
x-5\right)  ^{2}}{\left(  x-4\right)  ^{2}\left(  x+2\right)  }\qquad$b)
$\left(  x+1\right)  \allowbreak\dfrac{\left(  x-5\right)  ^{2}}{\left(
x-4\right)  ^{2}\left(  x-2\right)  }$\newline\qquad c) $\left(  x-1\right)
\allowbreak\dfrac{\left(  x-5\right)  ^{2}}{\left(  x-4\right)  ^{2}\left(
x+2\right)  }\qquad$d) $\left(  x+1\right)  \allowbreak\dfrac{\left(
x+5\right)  ^{2}}{\left(  x-4\right)  ^{2}\left(  x+2\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{6}x^{4}-9}{x^{2}-16}}{\dfrac{a^{4}x^{2}+9}{x^{2}+x-20}}%
\]
se obtiene: \newline\qquad\medskip a) $\allowbreak\left(  x+5\right)
\dfrac{a^{6}x^{4}-9}{\left(  a^{4}x^{2}+9\right)  \left(  x+4\right)  }$\qquad
b) $\left(  x-5\right)  \dfrac{a^{12}x^{4}-9}{\left(  a^{4}x^{2}+9\right)
\left(  x-4\right)  }$\newline\medskip\qquad c) $\left(  x+5\right)
\dfrac{a^{6}x^{4}-9}{\left(  a^{4}x^{2}+9\right)  \left(  x-4\right)  }$\qquad
d) $\left(  x-5\right)  \dfrac{a^{6}x^{4}-9}{\left(  a^{4}x^{2}+9\right)
\left(  x+4\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{8}x^{4}-81}{x^{2}-9}}{\dfrac{a^{2}x^{2}+8}{x^{2}+2x-15}}%
\]
e obtiene: \newline\medskip a) $\allowbreak\left(  x+5\right)  \dfrac
{a^{8}x^{4}-81}{\left(  a^{4}x^{2}+8\right)  \left(  x+3\right)  }$\qquad b)
$\left(  x-5\right)  \dfrac{a^{8}x^{4}-81}{\left(  a^{4}x^{2}+8\right)
\left(  x+3\right)  }$\newline c) $\left(  x-5\right)  \dfrac{a^{8}x^{4}%
-81}{\left(  a^{6}x^{2}+8\right)  \left(  x-3\right)  }$\qquad d) $\left(
x+5\right)  \dfrac{a^{8}x^{4}-81}{\left(  a^{6}x^{2}+8\right)  \left(
x+3\right)  }$\bigskip

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{2}x^{4}-25}{x^{2}-4}}{\dfrac{a^{8}x^{2}+16}{x^{2}+2x-8}}%
\]
se obtiene: \newline\qquad\medskip a) $\allowbreak\left(  x+4\right)
\dfrac{a^{2}x^{4}-25}{\left(  a^{8}x^{2}+16\right)  \left(  x+2\right)  }%
$\bigskip\qquad b) $\left(  x-4\right)  \dfrac{a^{2}x^{4}-25}{\left(
a^{8}x^{2}+16\right)  \left(  x-2\right)  }$\bigskip\newline\medskip\qquad c)
$\left(  x-4\right)  \dfrac{a^{2}x^{4}-25}{\left(  a^{8}x^{2}+16\right)
\left(  x+2\right)  }$\bigskip\qquad d) $\left(  x+4\right)  \dfrac{a^{2}%
x^{4}-25}{\left(  a^{6}x^{2}+16\right)  \left(  x-2\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{2}x^{2}-49}{x^{2}-25}}{\dfrac{a^{4}x^{2}+7}{x^{2}-3x-10}}%
\]
se obtiene: \newline\qquad\medskip a) $\left(  x+2\right)  \dfrac{a^{2}%
x^{2}-49}{\left(  a^{4}x^{2}+7\right)  \left(  x+5\right)  }$\qquad b)
$\left(  x-2\right)  \dfrac{a^{2}x^{2}-49}{\left(  a^{4}x^{2}+7\right)
\left(  x+5\right)  }$\newline\medskip\qquad c) $\left(  x-2\right)
\dfrac{a^{2}x^{2}-49}{\left(  a^{4}x^{2}+7\right)  \left(  x-5\right)  }%
$\qquad d) $\left(  x+2\right)  \dfrac{a^{4}x^{2}-49}{\left(  a^{4}%
x^{2}+7\right)  \left(  x-5\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{4}x^{2}-25}{x^{2}-4}}{\dfrac{a^{4}x^{2}+8}{x^{2}+3x-10}}%
\]
se obtiene: \medskip\newline\qquad\medskip a) $\left(  x+5\right)
\dfrac{a^{4}x^{2}-25}{\left(  a^{4}x^{2}+8\right)  \left(  x+2\right)  }%
$\bigskip\qquad b) $\left(  x-5\right)  \dfrac{a^{4}x^{2}-25}{\left(
a^{2}x^{2}+8\right)  \left(  x-2\right)  }$\bigskip\newline\medskip\qquad c)
$\left(  x-5\right)  \dfrac{a^{4}x^{2}-25}{\left(  a^{2}x^{2}+8\right)
\left(  x+2\right)  }$\bigskip\qquad d) $\allowbreak\left(  x+5\right)
\dfrac{a^{4}x^{2}-25}{\left(  a^{4}x^{2}+8\right)  \left(  x-2\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{2}x^{4}-36}{x^{2}-1}}{\dfrac{a^{2}x^{2}+6}{x^{2}-4x-5}}%
\]
se obtiene: \newline\qquad\medskip a) $\left(  x-5\right)  \dfrac{a^{2}%
x^{4}-36}{\left(  a^{2}x^{2}+6\right)  \left(  x-1\right)  }\allowbreak$\qquad
b) $\left(  x+5\right)  \dfrac{a^{2}x^{4}-36}{\left(  ax^{2}+6\right)  \left(
x-1\right)  }$\newline\medskip\qquad c) $\left(  x+5\right)  \dfrac{a^{2}%
x^{4}-36}{\left(  a^{2}x^{2}+6\right)  \left(  x+1\right)  }$\qquad d)
$\left(  x-5\right)  \dfrac{a^{2}x^{4}-36}{\left(  ax^{2}+6\right)  \left(
x+1\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{2}x^{2}-16}{x^{2}-9}}{\dfrac{a^{4}x^{4}+6}{x^{2}-x-12}}%
\]
se obtiene: \newline\qquad\medskip a) $\allowbreak\left(  x-4\right)
\dfrac{a^{2}x^{2}-16}{\left(  a^{4}x^{4}+6\right)  \left(  x-3\right)  }%
$\qquad b) $\left(  x+4\right)  \dfrac{a^{2}x^{2}-16}{\left(  a^{4}%
x^{4}+6\right)  \left(  x-3\right)  }$\newline\medskip\qquad c) $\left(
x+4\right)  \dfrac{a^{2}x^{2}-16}{\left(  a^{2}x^{4}+6\right)  \left(
x-3\right)  }$\qquad d) $\left(  x-4\right)  \dfrac{a^{2}x^{2}-16}{\left(
a^{2}x^{4}+6\right)  \left(  x+3\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{4}x^{4}-9}{x^{2}-16}}{\dfrac{a^{8}x^{4}+6}{x^{2}+x-12}}%
\]
se obtiene: \newline\qquad\medskip a) $\allowbreak\left(  x-3\right)
\dfrac{a^{4}x^{4}-9}{\left(  a^{8}x^{4}+6\right)  \left(  x-4\right)  }$\qquad
b) $\left(  x+3\right)  \dfrac{a^{4}x^{4}-9}{\left(  a^{4}x^{4}+6\right)
\left(  x-4\right)  }$\newline\medskip\qquad c) $\left(  x-3\right)
\dfrac{a^{4}x^{4}-9}{\left(  a^{8}x^{4}+6\right)  \left(  x+4\right)  }$\qquad
d) $\left(  x+3\right)  \dfrac{a^{4}x^{4}-9}{\left(  a^{4}x^{4}+6\right)
\left(  x+4\right)  }$\newline

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{2}x^{2}-16}{x^{2}-25}}{\dfrac{a^{4}x^{4}+10}{x^{2}+4x-5}}%
\]
se obtiene: \newline\qquad a) $\left(  x-1\right)  \dfrac{a^{2}x^{2}%
-16}{\left(  a^{4}x^{4}+10\right)  \left(  x-5\right)  }\allowbreak$\qquad b)
$\left(  x+1\right)  \dfrac{a^{2}x^{2}-16}{\left(  a^{2}x^{2}+10\right)
\left(  x+5\right)  }$\bigskip\newline c) $\left(  x-1\right)  \dfrac
{a^{2}x^{2}-16}{\left(  a^{4}x^{4}+10\right)  \left(  x+5\right)  }$\qquad d)
\bigskip$\left(  x+1\right)  \dfrac{a^{2}x^{2}-16}{\left(  a^{2}%
x^{2}+10\right)  \left(  x-5\right)  }$

Al simplificar completamente la expresi\'{o}n:%
\[
\dfrac{\dfrac{a^{4}x^{2}-9}{x^{2}-25}}{\dfrac{a^{4}x^{4}+7}{x^{2}+2x-15}}%
\]
se obtiene: \newline\qquad\medskip a) $\allowbreak\left(  x-3\right)
\dfrac{a^{4}x^{2}-9}{\left(  a^{4}x^{4}+7\right)  \left(  x-5\right)  }$\qquad
b) $\left(  x+3\right)  \dfrac{a^{4}x^{2}-9}{\left(  a^{4}x^{4}+7\right)
\left(  x+5\right)  }$\newline c) $\left(  x-3\right)  \dfrac{a^{4}x^{2}%
-9}{\left(  a^{4}x^{2}+7\right)  \left(  x+5\right)  }$\qquad d) $\left(
x+3\right)  \dfrac{a^{4}x^{2}-9}{\left(  a^{4}x^{2}+7\right)  \left(
x-5\right)  }$


\end{document}